Specifically for a piston general aviation aircraft, is there a recommended distance from the runway to fly the downwind leg? Does this change based on the speed of the aircraft?
Most instructors say that (in a low wing plane) you should see the runway on the tip of the wing or between the tip and 1/4 in the wing. AOPA has a nice over view of non towered airports here. This FAA brief states it should be flown 1/2 to 1 mile out (page 7-4 of FAA Airplane Flying Handbook, FAA-H-8083-3B).
This leg should be approximately 1/2 to 1 mile out from the landing runway, and at the specified traffic pattern altitude.
There are multiple considerations, among them:
- Other aircraft in the pattern (that may be slower or faster than you): you want to maintain your position, not getting too close to planes ahead of you, nor slowing down planes behind you.
- The descent rate of your aircraft: I was taught to descend 25% from TPA on downwind, 25% on base, and 50% on final. (typically from a 1,000 ft TPA, that is 250ft / 250ft / 500ft)
- The turning rate of your aircraft: You want to make rectangular shaped patterns. If you are too close, your patterns will be more oval shaped. If you are too far, you will have a very long base leg.
"Within gliding distance" is one common rule that many instructors teach. It would be embarrassing to have an engine failure in the pattern and not make it to the runway :-) More seriously, you tend to make a lot of configuration changes in the pattern so the risk of something going wrong is higher, therefore within gliding range is usually a good place to be.
That doesn't mean being in a position to glide the remaining downwind, base and final legs to land neatly on the numbers: it means gliding to somewhere on the runway you can safely land (or even to a taxiway if need be). (The FAA's commercial pilot test standards require the applicant to glide to a landing from the downwind leg starting at 1000 AGL.)
Of course, there are lots of variables and you may have to fly a wider (or tighter) pattern at certain times or at certain airports for any number of reasons: traffic, ATC instructions, noise abatement etc.